SOLUTION: a clock reads 5:30 a) what is the radian measure of the smaller angle between the hour and the minute hand b) what is the linear speed of the tip of the minute hand on a clock i

Question 812535: a clock reads 5:30
a) what is the radian measure of the smaller angle between the hour and the minute hand
b) what is the linear speed of the tip of the minute hand on a clock if that hand is 5cm long
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
a clock reads 5:30
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what is the radian measure of the smaller angle (A) between the hour and the minute hand?
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the hour hand is at h radians clockwise from 12 noon
h = (5/12) * 2 * pi ~= 2.618
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the minute hand is at m radians clockwise from 12 noon
m = (6/12) * 2 * pi ~= 3.142
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A = 3.142 - 2.618 = 0.524 radians
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what is the linear speed of the tip of the minute hand on a clock if that hand is 5 cm long
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s = d / t
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C = 2 * pi * R = 2 * pi * 0.05 = 0.31416 m/rev
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angular speed = (1 rev / 60 min) * (1 min / 60 sec) = 1/3600 rev/sec
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linear tip speed = (0.31416 m/rev) * (1/3600 rev/sec) = 8.727 * 10^-5 m/sec
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